Subsemigroups of an amenable group
Author:
Joe W. Jenkins
Journal:
Proc. Amer. Math. Soc. 26 (1970), 226-227
MSC:
Primary 20.93; Secondary 28.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262405-2
MathSciNet review:
0262405
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Abstract | References | Similar Articles | Additional Information
Abstract: The following example is presented. $G$ is a nondiscrete locally compact amenable group. $H$ is a subgroup of $G$ with zero Haar measure such that if $g \in G \sim H$ then (i) there is a subsemigroup $S = \bigcup \nolimits _{n = 0}^\infty {{I_n}}$ of $G$ where the ${I_n}’s$ are open pairwise disjoint ideals of $S$ (all right- or all left-ideals) and (ii) $g \in {I_0}$.
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- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
- M. Hochster, Subsemigroups of amenable groups, Proc. Amer. Math. Soc. 21 (1969), 363–364. MR 240223, DOI https://doi.org/10.1090/S0002-9939-1969-0240223-0
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Keywords:
Amenable group,
subsemigroup,
open disjoint right(left-) ideals,
free subsemigroup
Article copyright:
© Copyright 1970
American Mathematical Society